1College of Mathematics and Physics, Chongqing University of Posts and Telecommunications, Chongqing 400065, China2Key Laboratory of Industrial Internet of Things & Networked Control of Ministry of Education, Chongqing University of Posts and Telecommunications, Chongqing 400065, China3College of Applied Sciences, Beijing University of Technology, Beijing 100124, China

Abstract

This paper is concerned with a nonlinear fractional differential equation involving Caputo derivative. By constructing the upper and lower control functions of the nonlinear term without any monotone requirement and applying the method of upper and lower solutions and the Schauder fixed point theorem, the existence and uniqueness of positive solution for the initial value problem are investigated. Moreover, the existence of maximal and minimal solutions is also obtained.